Sen. Robert Bennett of Utah faces a growing list of Republican challengers.

(CNN) - Add another name to the growing list of Republicans challenging Sen. Robert Bennett of Utah, who's battling this year for a fourth term.

Former Republican Rep. Merrill Cook of Utah is scheduled Thursday to announce a primary challenge to Bennett. Cook held Utah's 2nd Congressional District for two terms, from 1997 to 2001. He lost his party's nomination in the 2000 election and the GOP lost the seat to Democrat Jim Matheson, who still holds the office.

Besides fighting against the overall anti-incumbent mood, Bennett also faces anger by many conservatives for his votes in 2008 in favor of the so-called Wall Street bailouts and last year's vote on bailing out the major American auto makers.

The fiscally conservative Club for Growth is working to defeat Bennett. So is FreedomWorks, another national organization that backs fiscally conservative causes. But Bennett has the backing of the National Republican Senatorial Committee, which as a rule supports Republican incumbents running for re-election.